Answer:
x = 424.3
Explanation:
we will answer this in 2 parts
first, we will prove the triangle is equilateral, using the known sum of all angles in a triangle.
then, we will find x using pythagorean theorem.
there is another way, involving trigonometric functions, i will show it too, at the end.
first, this is a right triange, as given in the drawing. so the known angles are 90 degrees and 45 degrees, leaving the third angle to be 45 as well.
this means the triangle is equilateral, so the sides of it are x, x, 600
now, since it is a right triangle, we can apply the pythagorean theorem, we get: x² + x² = 600²
from this we get:
2x² = 360000
x² = 180000
x = √180000 = 424.264
as we are asked to round to the nearest tenth, we write:
x = 424.3
bonus way - trigonometric functions
in a right triangle, the ratio between a side and the hypotenuse, is cos(α) where α is the angle between them, meaning:
x/600 = cos(45°)
and:
x = 600 × cos(45°) = 424.3